The velocity particle distributions measured in-situ in space plasmas deviate from Maxwellian (thermal) equilibrium, showing enhanced suprathermal tails which are well described by the standard Kappa-distribution (SKD). Despite its successful application, the SKD is frequently disputed due to a series of unphysical implications like diverging velocity moments, preventing a macroscopic description of the plasma. The regularized Kappa-distribution (RKD) has been introduced to overcome these limitations, but the dispersion properties of RKD-plasmas are not explored yet. In the present paper we compute the wavenumber dispersion of the frequency and damping or growth rates for the electromagnetic modes in plasmas characterized by the RKD. This task is accomplished by using the grid-based kinetic dispersion solver LEOPARD developed for arbitrary gyrotropic distributions [P. Astfalk and F. Jenko, J. Geophys. Res. 122, 89 (2017)]. By reproducing previous results obtained for the SKD and Maxwellian, we validate the functionality of the code. Furthermore, we apply the isotropic as well as the anisotropic RKDs to investigate stable electromagnetic electron-cyclotron (EMEC) and ion-cyclotron (EMIC) modes as well as temperature-anisotropy-driven instabilities, both for the case $T_\perp / T_\parallel > 1$ (EMEC and EMIC instabilities) and for the case $T_\perp / T_\parallel < 1$ (proton and electron firehose instabilities), where $\parallel$ and $\perp$ denote directions parallel and perpendicular to the local time-averaged magnetic field. Provided that the cutoff parameter $\alpha$ is small enough, the results show that the RKDs reproduce the dispersion curves of the SKD plasmas at both qualitative and quantitative levels. For higher values, however, physically significant deviation occurs.

中文翻译：

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正则化 Kappa 分布的平行电磁模式的线性色散理论

在空间等离子体中原位测量的速度粒子分布偏离了麦克斯韦（热）平衡，显示出增强的超热尾，标准 Kappa 分布 (SKD) 很好地描述了这一点。尽管 SKD 得到了成功的应用，但由于一系列非物理影响，例如发散速度矩，阻止了对等离子体的宏观描述，SKD 经常受到争议。引入了正则化 Kappa 分布 (RKD) 以克服这些限制，但尚未探索 RKD 等离子体的色散特性。在本文中，我们计算了以 RKD 为特征的等离子体中电磁模式的频率和阻尼或增长率的波数色散。这项任务是通过使用为任意回旋分布开发的基于网格的动力学色散求解器 LEOPARD 来完成的 [P. Astfalk 和 F. Jenko，J. Geophys。水库 122, 89 (2017)]。通过重现先前为 SKD 和 Maxwellian 获得的结果，我们验证了代码的功能。此外，我们应用各向同性和各向异性 RKD 来研究稳定的电磁电子回旋加速器 (EMEC) 和离子回旋加速器 (EMIC) 模式以及温度各向异性驱动的不稳定性，均适用于 $T_\perp / T_ \parallel > 1$（EMEC 和 EMIC 不稳定性），对于 $T_\perp / T_\parallel < 1$（质子和电子管不稳定性），其中 $\parallel$ 和 $\perp$ 表示平行和垂直于本地时间平均磁场。如果截止参数 $\alpha$ 足够小，结果表明 RKD 在定性和定量水平上都再现了 SKD 血浆的色散曲线。但是，对于更高的值，会出现物理上显着的偏差。